Learning-based controller for biotechnology processing, and method of using

ABSTRACT

The present invention relates to process control where some of the controllable parameters are difficult or impossible to characterize. The present invention relates to process control in biotechnology of such systems, but not limited to. Additionally, the present invention relates to process control in biotechnology minerals processing. In the inventive method, an application of the present invention manipulates a minerals bioprocess to find local exterma (maxima or minima) for selected output variables/process goals by using a learning-based controller for bioprocess oxidation of minerals during hydrometallurgical processing. The learning-based controller operates with or without human supervision and works to find processor optima without previously defined optima due to the non-characterized nature of the process being manipulated.

RELATED APPLICATION

This application claims priority to PCT application Ser. No.PCT\US99\10611, filed May 13, 1999 and provisional application Ser. No.60/085,420, filed May 13, 1998.

CONTRACTUAL ORIGIN OF THE INVENTION

This invention was made with United States Government support underContract No. DE-AC07-94ID13223, now Contract No. DE-AC07-99ID13727awarded by the United States Department of Energy. The United StatesGovernment has certain rights in the invention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to process control where at least some ofthe controllable parameters are difficult or impossible to characterizeor are unknown. More particularly, the present invention relates toprocess control in biotechnology. Even more particularly, the presentinvention relates to process control in biotechnology mineralsprocessing. In particular, an application of the present inventionrelates to a Bioexpert, learning-based controller for bioprocessalteration of minerals for hydrometallurgical processing.

2. Relevant Technology

Traditional process control technology uses mathematical models based onwell-defined and well-measured process states. Thereby, allowing the useof mathematical and well-understood control schemes or a series ofcontrol schemes, such as PID, Pole Placement, LQR/LTG, H^(∞), ARMA basedAdaptive Control, etc., to control the processes.

The biotechnology processing industry differs greatly from the moretraditional process control industry. This difference largely stems fromthe biological uncertainties and complexities of these systems. Theseuncertainties manifest themselves in a radically more complicatedprocess mechanisms and interactions to the process operator through theprocess' varying, undefinable and unpredictable nature. To this end,process control engineers in the biotech industry rely upon well-definedenvironmental process disturbances such as temperature, pH, electrodepotential, dissolved oxygen (DO), biomass density, and process flowrates to control the process. The bioprocess engineer acts torestrictively minimize the effects of environmental disturbances uponthe process due to the highly complex nature of a biosystem's reactionto these environmental disturbances.

In the mining industry, it is well known that an ore body will have bothgradual and radical changes in its composition throughout the ore body.As the ore is mined by the mining engineer, the process engineer mustwork closely with the mining engineer and the laboratory incharacterizing the chemical and physical nature of the ore body. Thisnewly developed characterization must be taken into account when the orebody is processed within the mill in order to continue the maximumproduction rates. Traditionally, this could involve recalculation of theprocess control parameters.

Additionally, a process engineer in the mining industry has the problemof transferring experience learned during the processing of one ore bodyto subsequent ore bodies that are to be processed. This problem is dueto the fact that ore bodies are usually highly site specific, i.e.composition specific, such that an entirely different process stream,processing approach, and process control scheme must be taken.

When a process engineer integrates bioprocessing with mineralsprocessing, the complexity of the combination often becomes greater thanthe sum of its parts. Particularly, a culture ofminerals-processing-microorganisms designed for the orerefining/leaching process will respond in complicated and unpredictableways to well-defined process disturbances such as temperature, pH, flowrate, and the like. It is these very facts that limits the use ofmathematical model based control schemes. Added to these complicationsof the bioprocessing field are the site-specific nature of each ore bodyand the sometimes radical variations of the chemical and physicalqualities of the ore within a single ore body.

Microbial treatment has been proven to be an economically viableapproach for the recovery of metals from some low-grade ores. Mineralsbioprocessing utilizes mixed cultures of iron- and sulfur-oxidizingacidophilic bacteria that cause the oxidation of mineral structures withthe concomitant liberation of metals from the ore. During biological oreoxidation, the microbial population change, the pH of the environmentcan increase or decrease, temperature generally increases, dissolved O₂and CO₂ concentrations decrease, and the concentration of metals in theleach liquor generally increases.

Due to the elevated temperatures (50 to 60° C. and higher) that can beachieved during biological heap-leaching operations, moderatelythermophilic bacteria are being considered as a way to extend theoperating temperature range and improve oxidation efficiency in theheaps. Moderately thermophilic bacteria have been isolated from acidiccoal dumps, ore deposits, mining operations, and hot springenvironments. They vary in their ability to oxidize iron, sulfur, andpyrite as well as in their ability to grow autotrophically orheterotrophically. Temperature, pH, metal concentration, O₂, CO₂, andpulp density are known to affect growth and mineral oxidation byacidophilic bacteria. However, in a minerals processing environment inwhich any number of physical and chemical parameters are changing, theextent to which these parameters interact and impact iron oxidation bymoderately thermophilic bacteria is unknown.

Moreover, minerals bioprocessing comprises very complex systems. Thephysical, chemical and biological components for minerals bioprocessingare not well characterized. In addition, the physical, chemical andmicrobial populations that are most favorable for optimum yields areoften unknown and are radically different from one mine site to thenext. More importantly, the physical and chemical conditions andmicrobial populations associated with these bioprocesses change withtime or, as evident in heap leaching operations, are spatially variable.The changing conditions and microbial populations make it vital that acontrol system be robust and able to adapt to these changes. Theseunderlining features rule out the use of traditional knowledge-based,neural network, fuzzy logic, and model-based intelligent controllers.Furthermore, traditional process optimization procedures may beinadequate to control highly variable, uncharacterized or unknowableconditions in minerals bioprocessing.

The minerals processing engineer using a bioprocess must stand around-the-clock watching of all process parameters in an attempt tooptimize minerals recovery while providing for the needs of themicroorganism culture using his heuristic process knowledge. Theminerals processing engineer routinely seeks correlation between inputand output in order to simplify processing decisions and to maximizerecovery. Many times the possible correlations in a microorganismminerals processing system become too many, too varied, and too complex.This makes the task of tracking any possible correlations betweenprocess inputs and goals an accounting nightmare, let alone a nearlyunfeasible task. Additionally, because biotechnology processes usemicroorganisms, the microorganism nursery itself can become the sourceof a processing problem wherein contamination or inoculation of aculture from other microorganisms can kill, render ineffective, or evencause an optimizing transmutation of the microorganisms that will affectthe biotechnology process in question.

What is needed is a method of controlling a process that can deal withthe complexity of a bio-minerals process and that adjusts to anuncharacterized and unknown set of environmental changes.

What is also needed in the art is a method of cultivating microorganismsfor biotechnology minerals processing that overcomes the problems of theprior art. What is also needed in the art is a method of mineralsprocessing by contacting and maintaining a microbial population withinan ore body. Additionally, mixed culture bioprocesses, such as thosefound in the mining industry, need to be developed and evaluated underconditions that will address more accurately the challenges of involvedin this field. Intelligent control technologies need to be designed tohandle the complexities inherent when examining multi-parametric effectson growth and metabolism by bacteria or when developing controlstrategies that are approximate for minerals processing bioprocesses.

SUMMARY AND OBJECTS OF THE INVENTION

An inventive stochastic reinforcement, learning-based control system wasdeveloped and applied to the supervision of uncharacterized, moderatelythermophilic bacterial culture in a continuous stirred tank reactor(CSTR). The inventive system had as a process goal, e.g. to optimize theproduction of oxidized iron.

The control system has the ability to select environmental set pointconditions, maintain those set points, analyze system states, and torecognize and diagnose instrument faults for the operator. Through theuse of a stochastic reinforcement learning algorithm, the control systemhas the ability to adapt and optimize the uncharacterized process, suchas the iron oxidation process performed by the thermophilic bacteria,within a mathematical process model. The inventive system serves as anouter loop controller, deriving its information from a plurality ofinner loop controllers, sensor packages and a diagnostic system. Theinventive system issues set point control values, e.g. pH, dilutionrate, and temperature, to both traditional and intelligent inner loopcontrollers. Moreover, these inner loop controllers also function astiered systems. That is the first layer of inner loop controllers inturn drive second layer inner loop fuzzy-based pH and temperaturecontrollers, which also drives third layer inner loop fuzzy-based pumpcontrollers.

The inventive method may include a software module that is one componentof an hierarchical hardware and software system developed for theintelligent control of iron oxidation by or the cultivation of mineralsprocessing microorganisms in a CSTR. The control system may use on-linesensors and off-line measurements to determine the state of the systemand the state of the process goals. The inventive method is used todetermine what actions are required to maximize process goals. Theseactions are carried out by lower level controllers usingcomputer-controlled actuators, such as pumps, gas-flow valves, heaters,and stirrers.

The inventive method may use stochastic learning to determine what thesystem environmental/input parameters should be, based upon the currentstate and past history of the system. Lower-level fuzzy systems andstandard classical methods within the lower lever controllers may thenbe used to actuate those commands and perturb the system to achieve thedesired goals. The diagnostic system analyzes the sensor data forinconsistencies and provides a log of the system operation.

Identification of the state of the system precedes the decisions of howthe directly controllable parameters should be changed. These decisionsmay be based upon the control strategy and are carried out according tothe inventive method. Two such methods are described herein. The firstprocedure for process operation according to the inventive method may becarried out as follows:

1. Choose a new set of process parameters.

2. Run the system to steady state at a given set of conditions.

3. Determine process output parameter values.

4. Has the goal or goals been maximized for the current choice of setpoints?

If yes, then maintain the process (until a change occurs), go to 2.

If no, then return to 1.

The second procedure for process operation according to the inventivemethod may be carried out as follows:

1. Choose a set of process parameters.

2. Run the system to steady state at a given set of conditions.

3. Determine process output parameter values.

4. Change at least one process/environmental input parameter accordingto the inventive method.

5. Run the system to steady state under the at least one changed inputparameter.

6. Determine process output parameter values.

7. Has the goal or goals been maximized for the current choice of setpoints?

If yes, then choose a new set of process input parameters, differentfrom those last chosen and go to 2.

If no, then return to 4.

Working examples for both methods are described within the preferredembodiments. In specific the second method, mainly step 4, used aworking example based on flow rate, an input parameter and peakproduction, an output parameter. The flow rate was chosen based on theapproximate range of values that should bracket the peak productionvalue using an expert system and an optimization algorithm. The initialflow rate was chosen by the operator, alternatively the inventive systemcontroller was set to the last best value found or a default value thatis in the center of the range. The second value was chosen to be 50%higher than the first value. The third value was chosen to be about 50%higher than the first value if the production rate increased.Alternatively, the third value was chosen to be about 33% lower than thefirst value if the production rate decreased.

After three or more different flow rate settings the optimizationalgorithm, a second-order polynomial fit was made to the data and theflow rate for maximum productivity was found from this function. Theprocess terminated when the flow rate for the estimated maximumproductivity was within the specified tolerance of the last trial.

In order to choose a new set of process parameters, a stochasticlearning scheme was used to determine the temperature, pH, and ironinlet concentration. The temperature, pH, and iron inlet concentrationwere each given an inventive initial two-sided Gaussian distributionwith defined limits. The low pH limit was based on what was expected tobe the lowest pH at which growth would occur at a rate that could beaccommodated without going to extremely low flow rates (outside of thelow level controllers abilities) and, moreover, extremely long testingperiods. The higher pH limit was the highest value that would not resultin the precipitation of iron-hydroxides. The temperature range was basedon the result of an experiment which examined the effects of temperatureon biomass growth and iron oxidation. The lower inlet iron concentrationwas based on the lower flow limits of the flow equipment. The higherinlet iron concentration was based on the concentration that was used inthe enrichment of a moderately thermophilic culture from a miningoperation.

The center for these distributions were used as the initial set points.The initial widths of the distributions were chosen to span reasonableoperating values for each parameter. When a new set point (pH,temperature,inlet iron concentration) was required as in Step 7 of thecontrol strategy, a random number generator based on the above inventivedistributions was used to select the new set points. The stochasticlearning took place by adjusting the inventive distributions, mean, andcomposition standard deviation, depending on the relative productionrates. If the rate improved with the new values, the center of thedistribution was shifted to the new value and the width was increased inthe direction of the change, while the width in the opposite directionwas reduced. However, if the rate did not improve, the center of thedistribution did not change, and the width in the direction of thechange was decreased, as before the opposite direction was increased.The steps of the inventive algorithm may be illustrated in code asfollows:

When at least one of the currently monitored process goals is betterthan the best recorded of the same, at least one of the process goals,then

When the best set point is less than the current set point then

increase the positive distribution width by a prescribed function whichis based on at least the current set point and the best set point,decrease the negative width by the function or another function, resetthe best set point to the current set point, and move the distributionto reflect the new best set point

Otherwise

decrease the positive distribution width by a prescribed function whichis based on the current set point and the best set point, likewiseincrease the negative width by said function or another function, resetthe best set point to the current set point, and move the distributionto reflect the new best set point

Otherwise

When the best set point is less than the current set point then

decrease the positive distribution width by a prescribed function whichis based on the current set point and the best set point, increase thenegative width by the function or another function

Otherwise

increase the positive distribution width by a prescribed function whichis based on the current set point and the best set point, decrease thenegative width by the function or another function

Loop.

The combined effects of pH, temperature, and iron concentration ongrowth and iron oxidation by moderately thermophilic, acidophilicenrichment cultures were examined in a continuous culture. The inventivecontrol system was used to acquire and analyze the data then to selectand maintain the sets of conditions that were evaluated. Originally, thecultures had been derived from a heap-leaching operation by cultivationat 55° C. in an acidic medium (pH 1.8) containing yeast extract and iron(100 mM Fe²⁺). Data indicated that pH was important, but not the onlyparameter that affected iron oxidation and growth.

A relatively high pH in combination with a relatively low temperature,or a relatively low pH in combination with a relatively high temperatureresulted in moderate to high oxidation rates. However, the culturesappeared sensitive to the combined effects of a relatively high pH (pH1.84) and high temperature (51.5° C.). Under these conditions littlecell growth and iron oxidation were observed. In a mixed culturecontaining mesophilic and thermophilic bacteria, the computer learnedthat at pH 1.8, 45° C., and an inlet iron concentration of 30-35 mM weremost favorable for iron oxidation of the ore samples that were tested.

The results disclosed herein demonstrate an interactive effect betweenpH and temperature that impacted growth and iron oxidation by moderatelythermophilic bacteria. In addition, the present invention demonstratesthe use of an intelligent control system as a tool that can be used tounderstand the interactive effects of environmental parameters onmicrobial activity.

In the control of biological processes, the present inventiondemonstrates that intelligent sensing and control technologies can beused in situations in which conventional set point control strategiesare not adequate or are impossible due to the lack of mathematicalmodels required to implement them. The inventive system can handleuncertainty, qualitative knowledge, poorly or incompletely modeledprocesses, and unexpected events. In short, the inventive system is morerobust than traditional control strategies with these conditions. Theinventive system monitors the process itself and the product, as well asthe process parameters, and can control the final product quality usingmappings based on analytical models, numerical models, engineeringexperience, and qualitative operational knowledge. In short, theinventive system has been created to replace the humanoperator/engineer/scientist when optimization is required for auncharacterized system or process.

Accordingly, it is an object of the present invention to control asystem by an algorithm, wherein the system has intrinsic uncertainty,poorly or incompletely modeled process parameters, unpredictablychanging process extrema (i.e. maxima and minima), unexpected loadchange events, and the like.

It is also an object of the invention to provide a process controlsystem that optimizes processing in the face of undefined or poorlydefined process parameters. It is also an object of the invention toprovide a system that seeks a local optimum or local optima in a processin which elements of the process change in difficult-to-characterizeways. It is also an object of the invention to provide a process thatlearns from processing data and chooses weighted variable values betweenprocessing elements and products.

It is also an object of the present invention to provide a processcontrol system that uses biological components that are uncharacterizedat any given time and that are manipulated for process optimizationwithout correlated or rigorous models thereof.

It is also an object of the present invention to provide a system thatcombines the inventive method with minerals processing that usesmicroorganisms that overcomes the problems of the prior art.

It is also an object of the present invention to provide a processcontrol system that uses mineralogical components that areuncharacterized at any given time and that are manipulated for processoptimization without correlated or rigorous models thereof.

It is also an object of the present invention to provide a processcontrol system that uses a mixture of biological and mineralogicalcomponents, either or both of which are uncharacterized at any giventime, and that are manipulated for process optimization withoutcorrelated or rigorous models thereof.

These and other objects, features, and advantages of the presentinvention will become more fully apparent from the following descriptionand appended claims, or may be learned by the practice of the inventionas set forth hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the manner in which the above-recited and other advantagesand objects of the invention are obtained will be understood, a moreparticular description of the invention briefly described above will berendered by reference to a specific embodiment thereof which isillustrated in the appended drawings. Understanding that these drawingsdepict only typical embodiments of the invention and are not thereforeto be considered to be limiting of its scope, the invention will bedescribed and explained with additional specificity and detail throughthe use of the accompanying drawings in which:

FIG. 1 is a schematic of the inventive method that uses the inventivesystem as an outer loop controller, an inner loop controller thatoversees data acquisition and sends control statements to actuators, anda diagnostic system that sends state of the process messages to theouter loop controller and inner loop controller.

FIG. 2 is an example of a BioExpert operator display panel thatillustrates a non-limiting embodiment.

FIG. 3 is an example of a BioController operator display panel thatillustrates a non-limiting embodiment.

FIG. 4 is an example of a Diagnostic operator display panel thatillustrates a non-limiting embodiment.

FIG. 5a illustrates selection of a new set point, T₁, within a definedor generated distribution range according to the inventive method.

FIG. 5b illustrates the updating of the set point distribution range dueto an improvement in the process productivity by increasing the inputparameter, obtaining a favorable result, shifting the center of adistribution, and updating the right and left distributions according tothe inventive method.

FIG. 5c illustrates the updating of the set point distribution range dueto a new set point trial where the input parameter was increased,without an improvement in the process productivity, thus decreasing thewidth of the split distribution, or changing the limit that isapproached by the direction of the difference by decreasing it, for thedata range on the side of the data distribution toward which the inputparameter was shifted according to the inventive method.

FIG. 6a illustrates a complete set of the inventive control systemresponses during the over 5000 hours of experimental embodiment testingof the invention in which the pH, temperature, iron inlet (Fe²⁺), andflow rates were varied according to the inventive method. Symbols:pH(F), temperature (B), Fe²⁺ (J), flow rate (H).

FIG. 6b illustrates some process outputs/measurements that were used incalculating the process productivity response during the over 5000 hoursof experimental embodiment testing of the invention in which the pH,temperature, iron inlet (Fe²⁺), and flow rates were varied according tothe inventive method. Symbols: productivity (H), Biomass/Cells (J), Fe³⁺(B).

FIG. 7 illustrates a selected function for the flow rate optimizationalgorithm for flow rate choices for run A described in Table III givenbelow, according to the inventive method.

FIG. 8 illustrates a selected function for the flow rate optimizationalgorithm for flow rate choices for run C described in Table III givenbelow, according to the inventive method.

FIG. 9 illustrates a selected function for the flow rate optimizationalgorithm for flow rate choices for runs A & C described in Table IIIgiven below, according to the inventive method.

FIG. 10 illustrates a selected function for the flow rate optimizationalgorithm for flow rate choices for run D described in Table III givenbelow, according to the inventive method.

FIG. 11 illustrates a selected function for the flow rate optimizationalgorithm for flow rate choices for run E described in Table III givenbelow, according to the inventive method.

FIG. 12 illustrates a selected function for the flow rate optimizationalgorithm for flow rate choices for run F described in Table III givenbelow, according to the inventive method.

FIG. 13 illustrates a selected function for the flow rate optimizationalgorithm for flow rate choices for run G described in Table III givenbelow, according to the inventive method.

FIG. 14 illustrates a selected function for the flow rate optimizationalgorithm for flow rate choices for run H described in Table III givenbelow, according to the inventive method.

FIG. 15 illustrates continuous space plot for the composite data for allpractical tests for the inventive stochastic learning method two withvarying flow rate control. The size of the sphere is proportional to theproductivity and the shade of the sphere is the productivity of thereactor defined later in the embodiment equation 22. FIG. 15A: Thecontinuous space plot has been positioned to allow viewing of the datawith respect of temperature (X-axis), pH (Y-axis) and inlet ironconcentration (Z-axis). FIG. 15B: The continuous space plot has beenrotated to provide a top-down view which emphasizes the data in relationto inlet iron (Z-axis) and pH (Y-axis). FIG. 15C: The continuous spaceplot has been rotated to provide a top-down view which emphasizes thedata in relation to temperature (X-axis) and pH (Y-axis). FIG. 15D: Thecontinuous space plot has been rotated to provide a side view whichemphasizes the data in relation to inlet iron concentration (Z-axis) andthe temperature (X-axis).

FIG. 16 illustrates continuous space plot for the composite data for allpractical tests for the inventive stochastic learning method one withthe flow rate fixed at $7\quad {\frac{m}{mi}.}$

The size of the sphere is proportional to the productivity and the shadeof the sphere is the productivity of the reactor defined later in theembodiment of equation 22. FIG. 16A: The continuous space plot has beenpositioned to allow viewing of the data with respect of temperature(X-axis), pH (Y-axis) and inlet iron concentration (Z-axis). FIG. 16B:The continuous space plot has been rotated to provide a top-down viewwhich emphasizes the data in relation to inlet iron (Z-axis) and pH(Y-axis). FIG. 16C: The continuous space plot has been rotated toprovide a top-down view which emphasizes the data in relation totemperature (X-axis) and pH (Y-axis). FIG. 16D: The continuous spaceplot has been rotated to provide a side view which emphasizes the datain relation to inlet iron concentration (Z-axis) and the temperature(X-axis).

FIG. 17 illustrates a typical probability distribution function thatdemonstrates use of the inventive stochastic learning algorithm, wherean iron concentration decrease did not improve productivity, hence themean was not changed, the upper limit was not changed, and the lowerlimit was increased.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention relates to process control using a stochasticlearning algorithm that locally optimizes a process as environmental andreaction mechanism parameters change in ways that are difficult tocorrelate or characterize. For a process to be controlled by theinventive method, a set of processing/environmental parameters such astemperature, pH, aeration, E_(H), feed rate, etc., must exist and bedirectly or indirectly controllable so that these set point values maybe selected and changed in order to optimize the process. Processoptimization procedures according to the inventive method evaluate thesets of parameters that maximize a production rate and/or productquality while resisting instabilities and perturbations by selectingwhat set points should be used, based on the current state of theprocess and the product.

The inventive method demonstrated that the relationships between theprocess parameter space, the process states, and the product propertyspace, or inverse relationships are controllable without beingcorrelated or rigorously defined. Sensing systems determined the statesof the process as well as the products. Process models, when available,provided some of the relationships between the product properties andthe process parameters. The inventive method used the above informationto arrive at the various proper set points in order to optimize orachieve the set of process goals.

In order to better address the requirements for minerals bioprocessingcontrol strategies, this invention discloses the integration orhybridation of a learning-based intelligent system with conventionalbioprocess control technologies as a non-limiting example of applicationof the invention. This hybrid system was applied to an uncharacterizedmicrobial culture that was obtained from an acidic heap-leachingoperation. The operating objective was to evaluate the ability of theinventive hybrid control system, with its integral learning program, tocontrol and optimize a process for which little expert knowledge wasavailable.

Reference will now be made to the drawings wherein like structures willbe provided with like reference designations. It is to be understoodthat the drawings are diagrammatic and schematic representations of theembodiment of the present invention and are not necessarily drawn toscale.

Control Methods

According to the present invention, the inventive method includesrunning a system to a defined steady state. Along the way to reaching asteady state, a data range and standard deviations for controlparameters, both input and output, are established. Operatorintervention may be used to establish range limits. For example, if itis known that a microorganism will not live or thrive outside a certainparameter range, the operator may set the range limits accordingly. Nextstandard deviations may be initialized for each input parameter byrunning the system for a sufficient time period to gather data therefor.The inventive method may then run the system for another cycle and teststhe change in the productivity for a given input parameter. If theproduction of the system (tracking at least one output parameter) isbetter than the previous best production or a process improvementoccurs, the system sets up an algorithm of changing input parametersthrough its learning how input parameter perturbations affect outputparameters and process goals. According to the inventive method, analgorithm is used in which a plurality of input variables aremanipulated in parallel to find a local maximum in at least one outputparameter. The system to be controlled has no presupposed processingparameter optima at any given time as the system discovers local optimathroughout the course of the process and as conditions change. Anexemplary embodiment of the experimental invention follows.

Applied to a biochemical system in minerals processing, the inventivemethod has overcome the problems of the prior art by a stochasticlearning scheme in which the computer, without rigorous modeling, expertsystems, or even fuzzy logic, controls selected input parameters despitethe absence of well-defined knowledge of the particular type ofbacterial culture or cultures and despite rigorous characterization ofthe ore body in process.

Exemplary Embodiment

Biological System

Two iron-oxidizing bacterial cultures that thrive in acidic environmentswere used in this study. The cultures differed in their carbon sourcerequirements, their growth temperature range, and the amount of “expertknowledge” that was available. One culture was an uncharacterizedmoderately thermophilic culture that was obtained from a miningoperation by cultivation at 55° C. in an acidic medium (pH 1.8)containing yeast extract and iron. In contrast, the secondiron-oxidizing culture, Thiobacillus ferrooxidans, has been wellcharacterized in over 50 years of study. This bacterium uses carbondioxide as its carbon substrate and grows well in acidic medium (˜pH 2)within a temperature range of 20-32° C. There have been many studieswhich have examined the effects of parameters such as pH, temperature,air and CO₂ sparging rates, heavy metal concentration, and mediumcomposition on the metabolism of T. ferrooxidans. In addition, thebioenergetics and genetics involved with mineral oxidation have beenexamined in great detail and there have been a number of analyticalmodels developed which are used to describe mineral oxidation by thisbacterium.

Cultures

In a first specific example, two thermophilic enrichment cultures werederived from a gold leaching operation. The first enrichment culture wasused for the example that examined the effects of flow rate, thentemperature. The second enrichment culture was used for the example thatsimultaneously varied pH, temperature, and inlet iron concentration.Thiobacillus ferrooxidans, ATCC 23270, was used in combination with themoderately thermophilic culture for the mixed culture embodiment. Allcultures were grown in an acidic (pH 1.8) medium containing, per liter,(NH₄)₂SO₄, 0.4 g; MgSO₄X7H₂O, 0.25 g; K₂HPO₄, 0.04 g; yeast extract, 0.2g; and 50 mM FeSO₄. The FeSO₄ was added as a filter-sterilized solutionafter autoclaving the medium.

Initial Characterization

The bioreactor was operated at a temperature of 45° C., an aeration rateof 1 standard liter per minute (SLM), a pH of 2.0, and a stirrer speedof 400 rpm in acidic salts medium containing 50 mM FeSO₄. The bioreactorwas inoculated with a culture grown at 55° C. then operated in batchmode for approximately 2½ days by which time the culture obtained asuspended cell density of approximately 10₇ cells/ml. To determinerelative growth and iron oxidation rates, the bioreactor was operated incontinuous flow mode with flow rates, set by the inventors, that rangedfrom 6 to 13.5 ml/min (Dilution rate=D=0.265 to 0.596/hr). To examinethe effects of temperature, the bioreactor was operated in continuousmode with a flow rate of 7 ml/min (D=0.309/hr) and temperatures of 40°,30°, 50°, 45°, 55°, and 60° C. that were selected in that order by theinventors.

During the initial characterization, steady state determinations weremade by the inventive system using the following criteria: after setpoints or flow rate were changed, a minimum of 5 residence times mustelapse with at least 1 residence time between sampling events; redoxvalues, Fe²⁺ concentration, Fe³⁺ concentration, and cell numbers do notvary more than 10%; and total iron concentration (the sum of Fe²⁻+Fe³⁺values) are within 5% of the set point inlet iron concentration.

Considered Uncertainties

The majority of bioprocesses, particularly fermentation processes forthe food, pharmaceutical and specialty chemical industries, utilize purecultures that have been well described. At the start of this study, thenumber of distinct species present in the enrichment culture wasunknown. Furthermore, all that was known about the culture was thecultivation medium, relative growth rate and temperature range. Themetabolic mechanisms and yield coefficients for iron oxidation by theunchacterized culture were unknown. Thus, there was insufficientinformation to develop a model for the enrichment culture. Later in thisstudy the addition of the mesophilic organism Thiobacillus ferrooxidansincreased the complexity of the culture.

A process optimization procedure that simultaneously varied multipleparameters added another dimension of complexity of the system as wellas the uncertainty of how the microbial culture would react. Mostmicroorganisms are characterized or bioprocesses optimized by varyingone parameter at a time. This assumes that the effects of environmentalor bioprocess parameters such as pH, temperature, and nutrient levelsare decoupled. However, in a mining bioprocess, any number of parameterscan change. The metabolic response of microbial cultures when more thanone physical or chemical characteristic is changing is unknown.

System Hardware:

A 2 L bio reactor with a working volume of approximately 1,360 mL(BioFlow I, New Brunswick Scientific Co., Inc. Edison, N.J.) wasequipped with a stirrer, five liquid feeds, a heater, and sensors. Thebio reactor was modified to accept remote signals from the computercontrol system for heating and stirrer speed. On-line sensors, fittedinto the stainless steel head plate of the bio reactor, measured pH(Ingold Electrodes, Inc., Wilmington, Mass.), temperature (Cole-Parmer,Vernon Hills, Ill.), oxidation-reduction potential (Eh) (IngoldElectrodes, Inc.), and dissolved oxygen (Ingold Electrodes, Inc.). ThepH and dissolved oxygen probes were interfaced to the computer withtheir respective transmitters (model 2300 pH transmitter, and model 4300dissolved oxygen transmitter, Ingold Electrodes, Inc.). The redox andtemperature probes were interfaced to the computer directly. Gas massflow controllers were used for air (Sierra Instruments, Monterey,Calif.) and carbon dioxide (MKS Instruments, Andover, Mass.)

The computer system was a backplane chassis that was equipped with aSB586T series single-board computer (Industrial Computer Source, SanDiego, Calif.) supporting a 233-MHz Intel Pentium processor. The SCXI(Signal Conditioning eXtension for Instrumentation) system (NationalInstruments, Austin, Tex.) provided front-end signal conditioning to anAT-MIO-16 plug-in data acquisition (DAQ) board. The SCXI modules, alongwith the DAQ board, provided a total of 47 analog input, 26 analogoutput, and 4 digital input-output channels. The SCXI bus routed analog,digital, timing, and triggering signals between modules and DAQ board.An eight-port serial board was added to give a total of 10 RS-232 seriallines when combined with the computer's two ports. The computer and allthe instruments in the system were protected with a Fortressuninterruptible power supply (Best Power Technology, Inc., Nedecah,Wis.)

Measurements

Off-line measurements were made for biomass (cell counts), dissolvedorganic carbon, and ferrous (Fe²⁺) and ferric (Fe³⁺) iron. Off-linetitration of Fe²⁺ species with potassium dichromate or potassiumpermanganate was used to determine the concentration of ferrous iron.The concentration of ferric iron in solution was determined off-line byabsorption of Fe³⁺ at 304 nm. Cell counts were made by staining cellsfiltered onto black polycarbonate membrane filters with acridine orangeor fluorescein-conjugated wheat germ agglutinin. Off-line measurementsof dissolved organic carbon were performed by filtering samples (0.2 μm,Puradisc polypropylene filters, Whatman, International, Ltd., Maidstone,England) prior to analysis using an organic/inorganic carbon analyzer(TOC 5000, Shimadzu, Inc., Columbia, Md.).

On-line measurements were taken for Redox potential, which provided anestimate of the ferric to ferrous ion ratio, dissolved oxygen, pH, andtemperature. Measurements of total organic carbon (TOC) and dissolvedinorganic carbon (CO₂) were made hourly using an organic/inorganiccarbon analyzer (TOC 5000, Shimadzu, Inc) on samples that wereautomatically withdrawn from the bioreactor.

Control System Implementation Description

The intelligent hybrid control system software was designed to determineand maintain set point conditions, analyze system state, and diagnoseinstrument faults. The software was written with LabVIEW, a graphicalprogramming language (National Instruments Corporation, Austin, Tex.).LabVIEW provides a convenient user interface for the operator, as wellas a sophisticated language interface to the I/O boards for dataacquisition and control.

The intelligent hybrid control system, depicted in FIG. 1 consisted ofthree interacting software modules: the BioExpert Controller, theBioController, and the Diagnostics System. Associated with each programwas an operating panel with various controls, indicators, graphs, andlogs which provided information about the process at that control levelas seen in FIGS. 2-4. The BioExpert Controller software module was thesupervisory control module that integrated the information provided bythe BioController and the Diagnostic System into its control decisions.The BioExpert Controller determined and displayed the current conditionswithin the bio reactor. It selected flow rates and it selected theparameters to be evaluated. It also displayed and maintained the log ofproduction values. It also provided other information, e.g. set pointvalues and current on-line sensor data.

The BioExpert as seen in FIG. 2 was the software control module thatevaluated and supervised the bio reactor using data from theBioController and the Diagnostic System. Using the on-line and off-linedata in connection with messages concerning set points changes, theBioExpert determined whether the bio reactor was in transition, atsteady state, or being “washed out”. Furthermore, the BioExpert used astochastic learning procedure to determine what the system set points,such as pH, dilution rate, and temperature, should be during the nextcontrol step. This algorithm based its decisions on the current and pastproduction values collected from the available data obtained by theBioController and the Diagnostics message log. These new set points werethen sent to a “message board” for the human operator's confirmation andimplementation within the BioController. Next, the flow rate controllerwithin the BioExpert optimized the flow rates for the newly selected setpoints.

The BioController software module as seen in FIG. 3 was based on moretraditional set point controllers and data acquisition systems. TheBioController provided low-level set point control and acquired on-linesensor data inputs. It also allowed manual entry of off-line data, setpoint control values, time intervals for data acquisition, file namesfor data logging. Additionally, the BioController provided on/offswitches for taking sensors off-line for cleaning and calibration, anddisplayed on-line and off-line data in graphs. It also maintained thedata log and provided other information about the low-level operationthe system, e.g. file name, elapsed time, etc.

Moreover, the BioController regulated conditions usingcomputer-controlled pumps for nutrient feeds and pH control (acid andbase pumps), gas-flow valves, a heater, and a stirrer. It should benoted that these lower-level set point control systems were made up ofboth fuzzy logic and conventional PID based controllers. Temperature andpH were feedback-controlled parameters that were controlled with fuzzycontrollers. The pump controllers automatically re-calibrated to assureaccurate dilution rates and feed concentrations. Liquid level wasmaintained by a drain tube located on the side of the chemostat. Gasflow rates were controlled open-loop. On-line data such as pH,temperature, dissolved oxygen, and off-line data such as cell numbers,Fe²⁺, and Fe³⁺ values were acquired, maintained as data logs, andpresented as continually updated graphs on the computer screen as wellas to the BioExpert.

The Diagnostics software module as seen in FIG. 4 diagnosed sensor dataand automatically logged changes in set point and when sensors weretaken off-line for maintenance. It also allowed manual entry of messagesand posted errors, changes, and messages in a panel.

In addition, the Diagnostic software Module seen in FIG. 4 compared thesensor data with set-point values to determine if the data wereconsistent with the desired bio reactor operation. If not, a note wouldbe logged into the file and posted on the front panel of the module.When a direct measurement of a set point value was possible, e.g., pH ortemperature, the Diagnostics program compared the set point to themeasured value and if they differed by a preset percentage for asignificant period of time, a warning message was displayed to theoperator panel of the module. Because there was no direct measure ofr.p.m., indirect evidence was used to diagnose the failure of thestirrer. Diagnosis of stirrer failure was based on earlier observationsthat stirrer failure resulted in a dramatic decrease in dissolved oxygenand a dramatic increase in Redox values within one hour of stirrerfailure.

The Diagnostic software Module automatically logged computer-generatedmessages, such as those dealing with changes in set points and whensensors were taken off-line then returned to service after maintenanceand calibration. The Diagnostic software module also logged messagesthat were entered by the operated. All errors, changes, and messageswere posted on the front panel for the operator to view as well asrecorded to a log file. The Diagnostic software module communicated withthe BioExpert to inform it of set point changes that indicated a systemstate change.

Best Fit Control of Flow

The flow rate controller used within the BioExpert was a hybridsub-system based on an expert system and a best fit control concept. Theexpert system then selected the initial three flow rates for thebest-fit control algorithm, see below. The best-fit control conceptassumed that flow rate, F_(rate), versus productivity, P (defined inEquations 22-25), fit a parabolic curve for a fixed set of conditions:pH (SetPt_(current) ^(pH)); temperature (SetPt_(current)^(temperature)); and iron concentration (SetPt_(current) ^(Fe)). Usingthe expert system's three initial flow rates productivities the best fitcontroller could then solve for the flow rate that maximizes theparabolic productivity curve. As additional flow rate data was obtainedit was added to the initial data in each new best fit flow rate choice.

The flow rate expert system was defined by a prescribed function asfollows (Run information is given in Table III):

1. The initial flow rate, F_(rate) ¹ was selected by the operator forthe first controller parameter set, pH, etc. (Run A). Alternatively, theexpert system initialized its flow rate using the center of theallowable range, in this case $5\quad {\frac{ml}{\min}.}$

For the subsequent control parameter sets, the first flow rate evaluatedin each set of parameters was the last flow rate evaluated in theprevious set (SetPt_(current) ^(pH), SetPt_(current) ^(temperature),SetPt_(current) ^(Fe)). For example, the first flow rate evaluated inRun D, was the last flow rate evaluated in Run C.

2. The second flow rate was chosen using the following logic:

If $F_{rate}^{1} \leq {7\quad \frac{ml}{\min}}$

Then

F_(rate) ^(target)=1.5F_(rate) ¹

Else $F_{rate}^{target} = \frac{F_{rate}^{1}}{1.5}$

3. The third flow rate was chosen as:If  F_(rate)¹ ≤ F_(rate)²  ThenIf  P(F_(rate)¹) ≤ P(F_(rate)²)  ThenF_(rate)^(target) = 1.5F_(rate)² Else$F_{rate}^{target} = \frac{F_{rate}^{1}}{1.5}$ ElseIf  P(F_(rate)²) ≤ P(F_(rate)¹)  ThenF_(rate)^(target) = 1.5F_(rate)¹ Else$F_{rate}^{target} = \frac{F_{rate}^{2}}{1.5}$

4. For the subsequent flow rates the parabolic fitting algorithm wasused.

After three flow rates had been evaluated, the flow controller switchedfrom the expert system to a prescribed function that was the parabolicdata fitting algorithm. A least squares parabolic fit for productivity,P, verses flow rate, F_(rate), curve was obtained by solving thefollowing equation:

AB=Y  (1)

where $\begin{matrix}{{A = \begin{bmatrix}1 & F_{rate}^{1} & \left( F_{rate}^{1} \right)^{2} \\1 & F_{rate}^{2} & \left( F_{rate}^{2} \right)^{2} \\\quad & \vdots & \quad \\1 & F_{rate}^{current} & \left( F_{rate}^{current} \right)^{2}\end{bmatrix}}\quad} & (2)\end{matrix}$

 B=[b ₀ b ₁ b ₂]^(T)  (3)

Y=[P(F _(rate) ¹) P(F _(rate) ²) . . . P(F _(rate) ^(current))]^(T)  (4)

Equation 1 was solved using a Singular Value Decomposition (SVD) thatproduced the pseudo inverse of A on the left. The SVD is a very stablemethod for performing this operation, as well as a conceptually simplepseudo inverse can be obtained using it. The SVD decomposes the matrix Ainto: a set of generalized eigenvectors on the left, U; a diagonalmatrix, Δ, whose values represent the singular values of the matrix; anda set of generalized eigenvectors on the right of the matrix, V.

A=UΔV ^(T)  (5)

where the following properties hold:

U ^(T) U=1  (6)

VV ^(T)=1  (7)

V ^(T) V=1  (8)

Next the pseudo inverse on the left is defined as:

A _(left) ⁻¹ =VΔ*U ^(T)  (9)

where $\Delta^{*} = \frac{1}{\Delta \left( {i,i} \right)}$

for 1≦i≦size(Δ); that is, invert the singular values along the diagonal.

It is easily shown that the above inverse does in fact invert the matrixA if it is multiplied on the left.

A _(left) ⁻¹ AB=A _(left) ⁻¹ Y  (10)

Thus the solution to Equation (1) can be written as:

B=VΔ*U ^(T) Y  (10)

After a parabolic fit to the data was obtained, the critical point ofthe parabola was used to calculate the next flow rate target.

P _(target) =P(F _(rate) ^(target))=b ₀ +b ₁ F _(rate) ^(target) +b ₂(F_(rate) ^(target))²  (12)

$\begin{matrix}{\frac{P_{target}}{F_{rate}^{target}} = {{b_{1} + {2b_{2}F_{rate}^{target}}} = 0}} & (13)\end{matrix}$

$\begin{matrix}{F_{rate}^{target} = {- \frac{b_{1}}{2b_{2}}}} & (14)\end{matrix}$

As new flow rates were issued and new fits were calculated, the fitsconverge on the optimal choice of the flow rate for the given set ofparameters. As the BioExpert changed the set points pH (SetPt_(current)^(pH)), temperature (SetPt_(current) ^(temperature)), and ironconcentration (SetPt_(current) ^(Fe)) the fitting algorithm reset andthe expert sub-system component of the flow controller restarted.

Stochastic Learning Controllers

A stochastic learning algorithm was used to determine the optimal pH,temperature, and iron concentration set points. Instead of a traditionalGaussian distribution, the distribution consisted of two half-Gaussiandistributions. The approach differed in that the learning algorithmunevenly biased the two-sided Gaussian distribution that was used tochoose the next set point. This was done to bracket the optimal solutionmore readily.

By using the mean of two half-Gaussian distributions, which are dividedat each one's traditional mean, the mean of this new distributionremains the same as a traditional Gaussian. $\begin{matrix}{\overset{\_}{x} = {\int_{- \infty}^{+ \infty}{x\quad {f_{x}(x)}{{x{\quad \quad}(15)}}}}} \\{= {{\frac{1}{\sqrt{2{\pi\sigma}_{L}^{2}}}{\int_{- \infty}^{\hat{m}}{x\quad ^{\lbrack\frac{- {({x - \hat{m}})}^{2}}{2\sigma_{L}^{2}}\rbrack}{x}}}} + \quad (16)}} \\{{\frac{1}{\sqrt{2{\pi\sigma}_{R}^{2}}}{\int_{\hat{m}}^{+ \infty}{x\quad ^{\lbrack\frac{- {({x - \hat{m}})}^{2}}{2\sigma_{R}^{2}}\rbrack}{x}}}}} \\{= {\frac{\hat{m}}{2} + {\frac{\hat{m}}{2}\quad (17)}}} \\{= {\hat{m}\quad (18)}}\end{matrix}$

In addition, the variance of the new distribution is also easilycalculated. $\begin{matrix}{{{var}(x)} = {\int_{- \infty}^{+ \infty}{\left( {x - \hat{x}} \right)^{2}{f_{x}(x)}{x}\quad (19)}}} \\{= {{\frac{1}{\sqrt{2{\pi\sigma}_{L}^{2}}}{\int_{- \infty}^{\hat{m}}{\left( {x - \hat{m}} \right)^{2}\quad ^{\lbrack\frac{- {({x - \hat{m}})}^{2}}{2\sigma_{L}^{2}}\rbrack}{x}}}} + \quad (20)}} \\{{\frac{1}{\sqrt{2{\pi\sigma}_{R}^{2}}}{\int_{\hat{m}}^{+ \infty}{\left( {x - \hat{m}} \right)^{2}\quad ^{\lbrack\frac{- {({x - \hat{m}})}^{2}}{2\sigma_{R}^{2}}\rbrack}{x}}}}} \\{= {\frac{\sigma_{L}^{2}}{2} + {\frac{\sigma_{R}^{2}}{2}\quad (21)}}}\end{matrix}$

The learning algorithm operated simultaneously for the three parametersthat were evaluated, pH (SetPt_(current) ^(pH)), temperature(SetPt_(current) ^(temperature)) and iron concentration (SetPt_(current)^(Fe)). The initial mean was chosen as a guess at where theproductivity, P, maximum was located (FIG. 5a, Table I). The initialwidths, i.e., the quasi variances of the distributions or standarddeviations (σ⁻ ^(x) and σ⁻ ^(x)), were chosen to span a reasonableoperating range for each parameter (FIG. 5a, Table I). The temperaturerange of 26° C. to 55° C. was based on experimental results obtained forthe bacteria. The concentration range of 15 to 100 mM was based on thedead limits of the peristaltic pumps, and expert knowledge concerningthe cultivation of the moderate thermophile. The pH range of 1.5 to 1.95was based on expert knowledge. Moreover, the lower limit was based onthe expected lowest pH at which growth would be at a rate sufficient toavoid extremely low flow rates. Avoiding low flow rates would avoid thedead-band limits of the pumps, minimize the possibility of washout, andavoid extremely long controller trials. The pH upper limit was chosen toavoid the formation of iron-hydroxides.

TABLE I Initial Gaussian Distributions (x, σ₊ ^(x), σ⁻ ^(x)). x{circumflex over (m)}^({overscore (x)}) σ₁₊ ^(x) σ¹⁻ ^(x) PH 1.8 0.5 0.5Temperature 45 5.0 5 Fe²⁺ + Fe³⁺ 50 15.0 15.0

The stochastic learning takes place by adjusting the distributions, e.g.mean and standard deviation, depending on the relative production rates.If the production rate improved with a tested set point, T₁, the newmean ({circumflex over (m)}) of the distribution was shifted to that setpoint. Also, at least one of the right and left widths, quasi variances,were changed to reflect the shift of the distribution towards theincrease in productivity (FIG. 5b). For example, if an increase intemperature resulted in an increase in productivity, the right side orupper limit of the Gaussian was increased and the left side or lowerlimit (representing the range towards lower temperature) was decreased.However, if the rate did not improve, the mean of the distribution didnot change, and the width of the distribution in the direction of theset point was decreased and the other side's width was increased (FIG.5c). To continue the example, if an increase in temperature did notresult in improved productivity, the mean remained the same, the rightside of the Gaussian was decreased, and the left side, towards the lowertemperatures was increased. The choice for each new set point was madeby using a random number generator based on the new two-sided Gaussiandistributions (such as T₁ in FIG. 5a).

FIG. 5 may be also described by applying the inventive algorithm to thefigures. The method of controlling the system comprises establishing asplit data distribution for at least one input variable. The split datadistribution is illustrated in FIG. 5a as comprising a standard Gaussiandistribution with T₀ as the mean which may be ascribed the value of N.The split data distribution has an initial standard deviation, an upperlimit and a lower limit as illustrated by the shape and end points ofthe Gaussian distribution. The method continues by running the systemand first measuring at least one output variable. The inventive methodcontinues by changing the value of the at least one input variable, inthis instance, temperature, from the mean T₀ to a new input variablevalue of T₁, or in a generic example, N+1. Next, a second measuring ofthe at least one output variable is taken. If the output variable isimproved, the inventive method proceeds by changing the mean of the atleast one input variable to the new input variable value T₁, or in ageneric example, N+1. The method continues by changing the upper limit,and changing the lower limit such that the split distribution reflectsthe original lower half of the Gaussian unchanged in height but shiftedby a value of T₁−T₀, or generically N+1−N, and the upper limit ischanged by a greater amount than the difference of T₁−T₀ or genericallyby an amount greater than N+1−N. Thus, the upper limit is changed, thelower limit is changed wherein the limit in the direction of thedifference is changed more than the limit that was distanced by thedirection of the difference. If the output variable is not improved, themean is not changed, the limit that lies in the direction distanced bythe direction of the difference is also not changed, and the limit inthe direction of the difference is decreased.

FIGS. 5b and 5 c illustrate specific examples of a temperature increaseand resulting respective favorable and unfavorable reactions by theinventive algorithm. In FIG. 5b, the temperature increase results in animproved output variable. Thus, the mean of the distribution is raisedto the temperature increase amount, T₁, the upper limit lies in thedirection approached by the difference, and the lower limit lies in thedirection distanced by the direction of the difference. Thus, the upperlimit is changed in an amount greater than the lower limit, and thelower limit is moved by only by an amount reflected by the difference ofthe change between the temperature T₀ and the temperature T₁. As thearea that is integrated under the split distribution must equal unity,it becomes clear that the upper limit in this example is changed by anamount greater than the amount of change in the lower limit.

Continuing with FIG. 5c, a temperature increase resulted in noimprovement of the output variable. Therefore, the mean of the datadistribution is not changed, the lower limit likewise is not changed,and the upper limit is decreased by an amount proportional to thedifference between T₀ and T₁. Similar to FIG. 5b, the area under thesplit distribution curve in FIG. 5c still nominally equals unity. Thus,the new distribution, although having the same mean, has a higherGaussian curve that is also narrower, or that has a smaller standarddeviation.

One basic stochastic control algorithm that is also used, i.e. x is pH,temperature, and iron concentration, was (see Tables I and II for eachindividual controller values):

Initialize the distributions comprises:

SetPt_(best) ^(x)={circumflex over (m)}^(x)

σ^(x)=σ_(i+) ^(x)

σ^(x)=σ_(i−) ^(x)

Repeat forever:

Select SetPt_(current) ^(x), evaluate P_(current) shown in the nextsection

Calculate the standard deviation change:${\Delta\sigma}^{x} = {{Sc}^{x}{\frac{{SetPt}_{current}^{x} - {SetPt}_{best}^{x}}{{SetPt}_{best}^{x}}}}$

If P_(current)>P_(best) then

If SetPt_(best) ^(x)<SetPt_(current) ^(x) then

SetPt_(best) ^(x)=SetPt_(current) ^(x)

P_(best)=P_(current)

{circumflex over (m)}^(x)=SetPt_(current) ^(x)

σ₊ ^(x)=σ₊ ^(x)+Δσ^(x) and σ⁻ ^(x)=σ⁻ ^(x)−Δσ^(x)

(increase the width of the right half of the distribution and decreasethe left half of the distribution)

Else

SetPt_(best) ^(x)=SetPt_(current) ^(x)

P_(best)=P_(current)

{circumflex over (m)}^(x)=SetPt_(current) ^(x)

σ₊ ^(x)=σ₊ ^(x)−Δσ^(x) and σ⁻ ^(x)=σ⁻ ^(x)+Δσ^(x)

(decrease the width of the right half of the distribution and increasethe width of the left half of the distribution)

Else

If SetPt_(best) ^(x)<SetPt_(current) ^(x) then

σ₊ ^(x)=σ₊ ^(x)−Δσ^(x) and σ⁻ ^(x)=σ⁻ ^(x)+Δσ^(x)

(decrease the width of the right half of the distribution and increasethe width of the left half of the distribution)

Else

σ₊ ^(x)=σ₊ ^(x)+Δσ^(x) and σ⁻ ^(x)=σ⁻ ^(x)−Δσ^(x)

(increase the width of the right half of the distribution and decreasethe left half of the distribution)

If σ₊ ^(x)<0.001 then σ₊ ^(x)=0.001

If σ⁻ ^(x)<0.001 then σ⁻ ^(x)=0.001

Loop.

In other words, the algorithm may be described as the following steps:

A method of operating a system with at least one input parameter and atleast one output parameter, comprising the steps:

establishing a data distribution for at least one input parameter, eachsaid data distribution having an upper fixed limit and a lower fixedlimit, a mean, and a standard deviation;

randomly changing each of said input parameter, updating its standarddeviation, and calculating the change in its standard deviation;

monitoring any change in said at least one output parameter;

if said change in said at least one output parameter constitutes asystem improvement:

quantifying a difference in said at least one input parameter;

if said difference in said at least one input parameter is an increase:

updating a positive standard deviation by adding the change in itsstandard deviation, and updating a negative standard deviation bysubtracting the change in its standard deviation;

if said difference in said at least one input parameter is a decrease:

updating a positive standard deviation by subtracting the change in itsstandard deviation, and updating a negative standard deviation by addingthe change in its standard deviation;

if said change in said at least one output parameter does not constitutea system improvement:

quantifying a difference in said at least one input parameter;

if said difference in said at least one input parameter is an increase:

updating a positive standard deviation by subtracting the change in itsstandard deviation, and updating a negative standard deviation by addingthe change in its standard deviation;

if said difference in said at least one input parameter is a decrease:

updating a positive standard deviation by adding the change in itsstandard deviation, and updating a negative standard deviation bysubtracting the change in its standard deviation;

if said positive standard deviation is less than about 0.001, ascribingthe value thereof to about 0.001;

if said negative standard deviation is less than about 0.001, ascribingthe value thereof to about 0.001; and

repeating said steps at least once.

Although a Gaussian distribution is used as an exemplary embodiment forthe present invention, other distributions may be used. Anothernon-limiting example includes a simple equilateral triangle distributionthat approximates a Gaussian distribution. Alternatively, thedistribution may be simply two quarter-circular arcs such that theentire distribution appears to be a semi-circular arc bisected at themean.

Additionally, a combination of distributions may be used such as aGaussian distribution for one portion and a nominal triangulardistribution for the other portion.

Where systems may react sharply to a given input variable change, thenew set point mean for the data distribution may be somewhere betweenthe old set point mean and the latest set point. This may have amoderating effect on output variable reaction.

TABLE II Scaling Factors for Δσ^(x) Calculations. X Sc^(x) pH 0.17Temperature 1.67 Fe²⁻ + Fe³⁻ 5.0

Supervision of Direct Control:

The BioExpert invoked a multi-step procedure that involved twointegrated subcontrollers; the flow rate controller and thestochastic-leaning controller. The variables that used to find theconditions for optimal production were pH, temperature (T), ironconcentration (Fe), and dilution rate (D) Productivity was defined as:

P=f(P _(iron))+(1−f)(P _(cells))  (22)

Where: $\begin{matrix}{f \leq 1} & (23) \\{P_{iron} = {\left\lbrack \frac{{Fe}^{3 +}}{{Fe}^{2 +} + {Fe}^{3 +}} \right\rbrack \times F_{rate}^{current}}} & (24) \\{P_{cells} = {\left\lbrack \frac{{Suspended}\quad {cells}\quad {numbers}}{1 \times 10^{8}} \right\rbrack \times F_{rate}^{current}}} & (25)\end{matrix}$

Bio reactor operation was as follows:

Set the algorithm step counter, k, to 0. Run the reactor to steady statefor a given temperature (SetPt_(current) ^(temperature)), pH(SetPt_(current) ^(pH)), iron concentration (SetPt_(current) ^(Fe)), andflow rate (F_(rate) ^(current)) combination

Calculate the production rate, P, (see equations 22-25)$P = {\left\lbrack \frac{{Fe}^{3 +}\quad {concentraction}}{{Fe}^{2 +} + {{Fe}^{3 +}{concentraction}}} \right\rbrack \times F_{rate}^{current}}$

Pick a new flow rate, F_(rate) ^(current), (by the Best Fit Control ofFlow method set forth above), k=k+1

Run the reactor to steady state

Calculate the production rate, P, (see equations 22-25)$P = {\left\lbrack \frac{{Fe}^{3 +}\quad {concentraction}}{{Fe}^{2 -} + {{Fe}^{3 +}{concentraction}}} \right\rbrack \times F_{rate}^{current}}$

Has the peak production rate, P, for this set point step (temperature,pH, and iron concentration) been reached?

If k≧4 and |P_(target)−P_(current)|≦1 ml Then

YES: Pick a new pH and temperature and go to Step 1

Else

NO: Go to Step 3

The identification of the state is one of the key steps used by theBioExpert. Using the on-line and off-line data and messages concerningchanges in set points, the BioExpert determined whether the bio reactorwas in transition, at steady state or being “washed out”. Reactor statedeterminations were made using the following three criteria. The reactorwas defined to be at steady state when the following conditions weremet. No set point changes were observed for at least 5 residence times.The Redox values change less than 10%. The Fe⁺² and Fe⁺³ concentrationschange less than 10%. And TOC changes less than 25%.

Likewise, the reactor was defined to be at washout when all of thefollowing conditions were met. More than two residence times had passedsince last set point change. TOC decreased by more than 50%. Redoxvalues decreased by more than 25%. Fe⁺² concentration increased by morethan 10%. And Fe⁺³ concentration decreased by more than 10%.

If the reactor was not at steady state or at washout, it was said to bein transition. This occurred whenever a set point was changed and theconditions for the other two states had not been met.

Residence time is the amount of time it takes for the volume of liquidwithin the reactor to be completely replaced. The residence time is thereciprocal of the dilution rate. The dilution rate, D, of the bioreactorexpressed in $\frac{1}{hr}$

is defined as: ${Flow}\quad \frac{Rate}{Volume}$

of the bioreactor. For example, the bioreactor used in this study had aworking volume of approximately 1360 $ml$. For a flow rate of$420\quad \frac{ml}{hr}$

the dilution rate would be ${.3088}\quad {\frac{1}{hr}.}$

Thus, the residence time $\left( \frac{1}{D} \right)$

for this example is 3.2 hours.

Results of Flow Rate Control

The bioreactor was operated using the learning-based control algorithm.The control decisions were made by the Supervisory Control System, whichvaried the values of pH, temperature, and iron concentration. Asdescribed above, steady state was defined as: Eh values, Fe²⁺ and Fe³⁺concentrations, and cell numbers do not vary more than 10%, with totaliron concentrations being within 5% of the set point. The weightingfunction for productivity was f=1, which optimized the productivity ofthe bioreactor for iron oxidation per unit time, see Equation 22.

The bio reactor was inoculated and operated in batch mode forapproximately 1 day during which time biomass reached a cell density of$2.7 \times 10^{7}\quad {\frac{cells}{ml}.}$

The bioreactor was operated in the continuous flow mode for a period ofapproximately 200 days (see FIG. 8) using the sets of conditions and theflow rates listed in Table III. Except when noted, the values reportedfor suspended cell density, Fe³⁺, and production $\frac{ml}{\min}$

are the values obtained when the bio reactor was operated at the flowrate that achieved the maximum iron production for that set ofconditions.

For Run A (pH 1.8; 45° C.; 50 mM Fe²⁺) productivity data for flow ratesof 4, 6, and $9\quad \frac{ml}{\min}$

were fitted to a polynomial and used predict that a flow of$7.01\quad \frac{ml}{\min}$

would result in optimum productivity (FIG. 9).

TABLE III Effects of Multi-Parameteric Changes on the Growth and IronOxidation by the Newmont Moderately Thermophilic Culture. Parameter SetValues at Maximum Productivity Run ° C. pH Inlet Iron (mM)$\begin{matrix}{{Flow}\quad {Rates}} \\\frac{ml}{\min}\end{matrix}$

$\begin{matrix}{Biomass} \\\frac{cells}{ml}\end{matrix}$

Fe³⁺ Fe²⁺ $\begin{matrix}{Productivity} \\\frac{mL}{\min}\end{matrix}$

A 45 1.8 50 4, 6, 9, 7.03*  7.6 × 10⁷ 45.08 6.95 6.31 B 51.5 1.84 47.157, 2* 2.91 × 10⁵ 4.24 40 0.19 C 45 1.8 50 7, 4.67, 10.5, 7.45* 7.33 ×10⁷ 42.88 8.7 6.193 D 40.7 1.9 34.48 7.45, 4.93, 11.1, 12, 11.2* 1.62 ×10⁷ 16.28 18.9 5.183 E 53.3 1.64 60.65 11.1, 7.4, 12, 9.6* IncompleteRun - No Data F 53.3 1.64 60.65 4.5, 7.5, 11.25, 9.17, 12, 8.52* 2.98 ×10⁷ 35.56 26.4 4.891 G 39.7 2.3 45.5 8.55, 5.73, 12, 12.75**, 15.4, 212.28 × 10⁷ 5.4 42.5 1.4 H 39.9 1.7 39.94 5.2, 7.8, 11.7, 9.19* 3.14 ×10⁷ 22.74 12.9 6.32 *Values obtained at the flow rate for which maximumproductivity was achieved. $12.75\quad \frac{ml}{\min}$

**Liquid feed system unable to deliver calculated flow rate. Values arefor flow rate of.

This flow rate was validated by the final run of$7\quad {\frac{ml}{\min}.}$

There was no curve fitting procedure for Run B (pH 1.84, 51.5° C., 47.15mM Fe²⁺) which was terminated by the operator due to washout even at thelower flow rate of $2.0\quad {\frac{ml}{\min}.}$

Run C (pH 1.8, 45° C. from near washout conditions (see FIG. 8). Thecomparison of data obtained for runs A and C (see FIG. 9) indicatedthere was a consistency in the behavior of the chemostat in spite of thefact that the microorganisms were subjected to an adverse set ofparameters.

During Run D, the computer had predicted that maximum productivity wouldoccur at $11.2\quad \frac{ml}{\min}$

(see FIG. 10). The final productivity for this run was a value of 5.183instead of 8.5 that was achieved at a flow rate of$11.1\quad {\frac{mls}{\min}.}$

Nevertheless, because the final curve fitting procedure using thecomplete set of data had a optimal flow rate that was comparable to theone that was predicted (11.2 mls), the data set was considered validatedand the computer selected the next set of parameters to evaluate.

Run E (see FIG. 11) was not completed due to a malfunction in the harddrive the computer. During Run F (see FIG. 12), the computer required 6flow rates to select and validate the maximum productivity. A rathershallow curve was obtained that did not have a strong maximum.Comparable productivity values were obtained at the similar flow ratesthat were evaluated in both Runs E and F.

Run G (see FIG. 13) illustrated the difficulty the control systemencountered when evaluating a set of parameters (pH 2.3, 39.7° C. and45.5 mM iron) that resulted in poor productivity. In this example, theoverall conversion of Fe²⁺ to Fe³⁺ was so low that productivity couldonly be improved by increasing flow rate. Because of the shape of thecurve, the BioExpert was unable to determine a flow rate at whichmaximum productivity was achieved based on the programmed curve fittingprocedure. The run was terminated by the human operators becauserequested flow rates had exceeded the pumping capacity of the smalltubing that was installed in the peristaltic pumps. Nevertheless, forpurposes of discussion and comparison to other runs, the data obtainedat the flow rate of 12.75 was utilized.

The behavior of the reactor in Run H (see FIG. 14), was such that themaximum productivity was easily predicted and validated according to theprogrammed procedure. The maximum productivity data for Runs A-H areplotted in a 3-dimensional figure in which the X, Y, and Z axes are thepH, temperature and inlet iron concentrations, see FIG. 15. The maximumproductivity for that run is indicated by coloration or the size of thesphere.

Results of Learning-Based Control

A learning-based supervisory control system, such as the one describedherein, would be applicable for any bioprocess for which there is littlea priori information, such as the problem selected for this study.Little was known about this iron-oxidizing culture other than it was“enriched” from a sample acquired from a heap leaching operation bycultivation at 55° C. in an acidic (pH 1.8) medium containing yeastextract and Fe²⁺. To acquire some expert knowledge about the behavior ofthis culture, the bioreactor was operated with the control decisionsmade by the human operator, i.e., change in flow rate and change intemperature, with steady state determinations using the intelligentcontrol system's criteria. This information was used to set theallowable environmental range used within the stochastic learningalgorithm, e.g. the maximum allowed pH. Such general limits are used toprotect the bacteria from an assumed killing environment. Similar limitsare used on more traditional control systems. For example, aircraft havea maximum allowed acceleration, which corresponds to a maximum G-force,that a structure may experience before structural failure occurs.

The interaction of the BioExpert software module with the BioControllersoftware module was comparable to other hierarchical systems that havebeen described in the literature. Due to the settling times for thesystem and the iterative approach to finding the optimal flow rate foreach environmental parameter set, a considerable amount of time wasrequired for each step of the stochastic learning algorithm.Consequently, it required approximately six to seven months to evaluatethe full controllers eight environmental parameter sets discuss withinthis paper, see Table III. Another set of runs, runs 16-24 in Table IV,was completed in a much shorter time period using the isolatedstochastic learning control system by operating the system without theflow rate optimization sub-controller. The flow rate controller was setto $7\quad {\frac{ml}{\min}.}$

TABLE IV Effects of Multi-Parametric Changes on the Growth and IronOxidation by the Newmont Moderately Thermophilic Culture (Near ConstantFlow Rate). Parameter Set Values at Steady State Run ° C. pH Inlet Iron(mM) $\begin{matrix}{{Flow}\quad {Rate}} \\\frac{ml}{\min}\end{matrix}$

$\begin{matrix}{{Biomass}\quad \times 10^{6}} \\\frac{Cells}{ml}\end{matrix}$

Fe³⁺ (mM) Fe²⁺ (mM) Fe³⁺/Fe²⁺ % Iron Oxidized $\begin{matrix}{Productivity} \\\frac{ml}{\min}\end{matrix}$

 1 40 2 50 7 9.9 21.96 29.20 0.75 42.9 3.005  2 30 2 50 7 4.71 19.6632.33 0.61 37.8 2.647  3 50 2 50 7 18.7 23.64 26.60 0.89 47.1 3.294  445 2 50 7 14.2 19.94 31.00 0.64 39.1 2.740  5 55 2 50 7 21.2 20.74 29.800.70 41.0 2.873  6 60 2 50 7 1.7 12.22 38.20 0.32 24.2 1.697  7 45 1.850 7.03 76 45.08 6.95 6.49 86.6 6.091  8 45 1.8 50 7 105 48.8 2.10 23.2495.9 6.711  9 51.5 1.84 47.15 7 4.4 10.27 37.75 0.27 21.4 1.497 10 451.8 50 7 82.9 43.12 8.40 5.13 83.7 5.859 11 45 1.8 50 7.45 73.3 42.888.70 4.93 83.1 6.193 12 40.7 1.9 34.48 7.4 29 27.7 6.15 4.50 81.8 6.06513 53.3 1.64 60.65 7.4 85.1 46.36 14.25 3.25 76.5 5.660 14 53.3 1.6460.65 7.5 70.4 48.32 15.25 3.17 76.0 5.701 15 39.9 1.7 39.94 7.8 31.526.92 14.38 1.87 65.2 5.084 16 32 1.7 50 7 35.8 22.04 29 0.76 43.2 3.02317 38.7 1.69 17.14 7 2.13 0.769 17 0.05 4.3 0.303 18 34 1.69 53.61 7 1.02.45 52 0.05 4.5 0.315 19 45 1.87 51.33 7 66.5 32.28 18.88 1.71 63.14.417 20 43 1.94 16.82 7 54.7 14.19 1.8 7.88 88.7 6.212 21 36.8 1.8531.05 7 23 16.14 15.50 1.04 51.0 3.571 22 45.9 1.87 21.74 7 83.8 20.661.38 15.03 93.8 6.563 23 43.6 1.8 28.9 7 45.9 27.04 1.53 17.73 94.76.626 24 44 1.81 34 7 44.8 34.2 1.43 24 96.0 6.720

The results shown in FIG. 15 for the combined stochastic and flow rateoptimization control system show that the assumption of coupledenvironmental parameters is correct. This is an important result, sincethe biological community tend to assume the decoupling of theenvironmental parameters as they investigate a new bacterium. In orderto speed the decision making process, as was mentioned above, the flowrate optimization controller was turned off, the productivity space forthis series of stochastic choices is shown in FIG. 16. A typicalprobability distribution function for this series within the stochasticlearning algorithm is shown in FIG. 17. It can be shown through examplesthat over time the stochastic learning algorithm's distributionfunctions practical support, shrink to approximate delta-dircafunctions. Once this occurs, the local maximum productivity for thebioprocess has been found. Although the data presented to date is notover a sufficient length of time for the distribution functions toshrink completely to a delta-dirca function, it is clear that thecontroller was progressing in that direction.

Illustrative Examples of the Algorithm

The present invention may be illustrated by three examples. In a firstexample, an input parameter is increased and a selected output orprocess goal is improved, or the selected output parameter or processgoal is not improved. In a second example, an input parameter isdecreased and a selected output parameter or process goal is improved,or it is not improved. In a third example, an input parameter isgenerically changed and a selected output parameter or process goal isimproved, or it is not improved

In the first example, a split Gaussian data distribution is established,by way of non-limiting illustration, for temperature, T. The splitGaussian data distribution has a mean of T₀, a standard deviation, anupper limit, and a lower limit. The system is run for a time period anda first measuring is taken on an output variable, by way of non-limitingillustration, for Fe³⁺. Next, the value of the temperature is changedfrom the mean, T₀, to a new amount, T₁ to create a difference: T₁−T₀.Next, a second measuring is taken on the same output variable, Fe³⁺. Ifthe output variable is improved, (i.e. increased), the mean, T₀, ischanged to T₁. The upper limit is changed by a first amount, and thelower limit is changed by the difference: T₁−T₀. The change of the upperlimit by the first amount is greater than T₁−T₀. The area under theGaussian curve remains nominally equal to unity. If the output variableis not improved, then the mean, T₀, is not changed, the upper limit isdecreased by an amount proportional to T₁−T₀, and the lower limit is notchanged.

In the second example, the input variable, T₀, is decreased to T₁ andthe output variable or process goal (e.g. Fe³⁺) is improved, or theoutput or process goal is not improved. The split Gaussian datadistribution is the same initially as in the first example. The systemis run for a time period and a first measuring is taken on an outputvariable, Fe³⁻. Next, the value of the temperature is changed from themean T₀ to a new amount, T₁ to create a difference: T₀−T₁. Next, asecond measuring is taken on the same output variable, Fe³⁺. If theoutput variable is improved (e.g. Fe³⁺ is increased), the mean, T₀, ischanged to T₁. The lower limit is changed by a first amount, and theupper limit is changed by the difference: T₀−T₁. The change of the lowerlimit by the first amount is greater than the difference of T₀−T₁. Thearea under the split Gaussian curve remains nominally equal to unity,however. If the output variable is not improved, then the mean, T₀, isnot changed. The lower limit is decreased by an amount proportional toT₀−T₁, and the upper limit is not changed.

The third example is generic as to the direction of change of the inputvariable and as to the type of data distribution that is used. In thisthird example, a method of controlling a system is provided byestablishing a split data distribution for at least one input variableT, the split data distribution has a mean of T₀, a standard deviation,an upper limit, and a lower limit. The system is run for a period oftime and first measuring is taken for the at least one output variable.The value of the input variable, T, is changed from the mean, T₀ to anew value, T₁ to create a difference: |T₀−T₁|. A second measuring of theat least one output variable is taken. If the output variable isimproved, the mean input variable, T₀ is changed to T₁, the upper limitof the data distribution is changed, and the lower limit of the datadistribution is changed. The limit that is approached by the directionof the difference between T₀ and T₁ is changed more than the limit thatis distanced by the difference between T₀ and T₁. If the output variableis not improved, then the mean, T₀ is not changed, the limit that isapproached by the direction of the difference between T₀ and T₁ ischanged by decreasing it proportional to |T₀−T₁|, and the limit that isdistanced by the difference between T₀ and T₁ is not changed.

Concluding Embodiment Remarks

In summary, the importance of proper control of multi-parametric effectson the growth and iron-oxidation by acidophilic, moderately thermophilicbacteria was demonstrated according to the inventive method. Thestandard assumption made in biological experimentation is that thebiological controls, i.e. the environmental parameters, are decoupled.This assumption allows for the search of an optimal productionenvironment through the mapping of the data space one parameter at atime. This control system was designed around the opposite assumption;primarily that the biological controls are coupled. Through the testingof this system, it has been shown that coupled parameters is the onlyplausible assumption that can be made for this biological system.

The current implementation of this invention appeared to function asdesired. Moreover, this reactor and control system provided a valuablereal world means for testing new and improved control system concepts inmodel less environments. This control system serves as an example ofwhat the microbiological research teams currently need for studyingnewly discovered uncharacterized microorganisms.

The present invention may be embodied in other specific forms withoutdeparting from its spirit or essential characteristics. The describedembodiments are to be considered in all respects only as illustrated andnot restrictive. The scope of the invention is, therefore, indicated bythe appended claims rather than by the foregoing description. Allchanges which come within the meaning and range of equivalency of theclaims are to be embraced within their scope.

We claim:
 1. A method of controlling a bioreactor comprising:establishing in an expert controller a split data distribution for atleast one input variable, the split data distribution having a mean of Nand a standard deviation, an upper limit, and a lower limit; running thebioreactor according to the at least one input variable as controlled bya biocontroller and first measuring at a diagnostic system at least oneoutput variable from the reactor; changing in the expert controller avalue of the at least one input variable from the mean to a new inputvariable value, N+1, to create a difference (N+1)−N; running thebioreactor according to the value of the it least one input variable ascontrolled by the biocontroller and second measuring at the diagnosticsystem the at least one output variable from the bioreactor, and if theat least one output variable is improved, in the expert controller:changing the mean of the at least one input variable to the new inputvariable value, N+1; changing the upper limit; and changing the lowerlimit, wherein a one of the upper and lower limit that is approached bythe direction of the difference is changed more than a one of the upperand lower limit that is distanced by the direction of the difference;and if the at least one output variable is not improved, in the expertcontroller: not changing the mean of the at least one input variable;changing a one of the upper and lower limit that is approached by thedirection of the difference by decreasing it; and not changing a one ofthe upper and lower limit that is distanced by the direction of thedifference.
 2. The method of controlling a bioreactor according to claim1, wherein when the at least one output variable comprises a plurality,the plurality including product productivity, P_(product), and biomassdensity, P_(biomass), further comprising: ascribing a relationshipbetween the product productivity and the biomass density according toP=f(P_(product))+(1−f)(P_(biomass)), wherein P is overall processproductivity and f is a weighting factor in a range from 0 to
 1. 3. Themethod of controlling a bioreactor according to claim 2 wherein theweighting factor, f, is varied comprising: when a present productivityof a first product is greater than its previous maximum productivity,then the weighting factor is increased; but when the weighting factor,as increased, is greater than 1, then the weighting factor is equal to1; when the present productivity of the first product is not greaterthan its previous maximum productivity, the weighting factor isdecreased; when a present productivity of a second product is greaterthan its previous maximum productivity, then the weighting factor isdecreased; when the present productivity of the second product is notgreater than its previous maximum productivity, the weighting factor isincreased; but when the weighting factor is greater than 1, then theweighting factor is equal to 1; and repeating the method at least once,wherein the weighting factor is a highest retained value thereof.
 4. Themethod of controlling a bioreactor according to claim 1, whereinchanging the value of the at least one input variable includes ascribinga random value thereto within a predetermined range.
 5. The method ofcontrolling a bioreactor according to claim 1, wherein one of the atleast one input variable is pH.
 6. The method of controlling abioreactor according to claim 4, wherein the predetermined range isdetermined by selecting at least one microorganism and determining a pHrange within which the at least one microorganism will remain viable. 7.The method of controlling a bioreactor according to claim 1, wherein oneof the at least one input variable is temperature.
 8. The method ofcontrolling a bioreactor according to claim 4, wherein the predeterminedrange is determined by selecting at least one microorganism anddetermining a temperature range within which the at least onemicroorganism will remain viable.
 9. The method of controlling abioreactor according to claim 1, wherein one of the at least one inputvariable is microorganism flow rate.
 10. The method of controlling abioreactor according to claim 4, wherein the predetermined range isdetermined by selecting at least one microorganism and determining amicroorganism flow rate range within which the at least onemicroorganism will resist reactor washout.
 11. The method of controllinga bioreactor according to claim 1, wherein changing the value of the atleast one input variable includes ascribing a random value thereto. 12.A method of controlling a reactor comprising: establishing in an expertcontroller a split data distribution for at least one input variable,the split data distribution having a mean of N, a standard deviation, anupper limit, and a lower limit; running the reactor according to the atleast one input variable as controlled by a biocontroller and firstmeasuring at a diagnostic system at least one output variable;increasing in the expert controller a value of the at least one inputvariable from the mean to a new input variable value, N+1; running thereactor according to the value of the at least one input variable ascontrolled by the biocontroller and second measuring at the diagnosticsystem the at least one output variable, and if the at least one outputvariable is improved, in the expert controller: changing the mean of theat least one input variable to the new input variable value, N+1;changing the upper limit; and changing the lower limit by an amountequivalent to the difference (N+1)−N, wherein the upper limit is changedby a value greater than N+1−N; and if the at least one output variableis not improved in the expert controller: not changing the mean of theat least one input variable; not changing the lower limit; anddecreasing the lower limit.
 13. The method of controlling a reactoraccording to claim 12, wherein when the at least one output variablecomprises a plurality, the plurality including product productivity,−P_(product), and biomass density, −P_(biomass), further comprising:ascribing a relationship between the product productivity and thebiomass density according to P=f(P_(product))+(1−f)(P_(biomass)),wherein P is overall process productivity and f is a weighting factor ina range from 0 to
 1. 14. The method of controlling a reactor accordingto claim 13, wherein the weighting factor, f, is varied comprising: whena present productivity of a first product is greater than its previousmaximum productivity, then the weighting factor is increased; but whenthe weighting factor, as increased, is greater than 1, then theweighting factor is equal to 1; otherwise the weighting factor isdecreased; otherwise when a present productivity of a second product isgreater than its previous maximum productivity, then the weightingfactor is decreased; otherwise the weighting factor is increased; butwhen the weighting factor is greater than 1, then the weighting factoris equal to 1; and repeating the method at least once, wherein theweighting factor is a highest retained value thereof.
 15. A method ofcontrolling a reactor comprising: establishing in an expert controller asplit data distribution for at least one input variable, the split datadistribution having a mean of N and a standard deviation, an upperlimit, and a lower limit; running the reactor according to the at leastone input variable as controlled by a biocontroller and first measuringat a diagnostic system at least one output variable from the reactor;decreasing in the expert controller a value of the at least one inputvariable from the mean to a new input variable value, N+1; running thereactor according to the value of the at least one input variable ascontrolled by the biocontroller and second measuring at the diagnostic,system the at least one output variable, and if the at least one outputvariable is improved, in the expert controller: changing the mean of theat least one input variable to the new input variable value, N+1;changing the lower limit by a first amount; and changing the upper limitby an amount equivalent to a difference (N+1)−N, wherein the lower limitis changed by a value greater than (N+1)−N; and if the at least oneoutput variable is not improved, in the expert controller: not changingthe mean of the at least one input variable; not changing the upperlimit; and increasing the lower limit.
 16. The method of controlling areactor according to claim 15, wherein when the at least one outputvariable comprises a plurality, the plurality including productproductivity, −P_(product), and biomass density, −P_(biomass), furthercomprising: ascribing a relationship between the product productivityand the biomass density according toP=f(P_(product))+(1−f)(P_(biomass)), wherein P is overall processproductivity and f is a weighting factor in a range from 0 to
 1. 17. Themethod of controlling a reactor according to claim 16, wherein theweighting factor, f, is varied comprising: when a present productivityof a first product is greater than its previous maximum productivity,then the weighting factor is increased; but when the weighting factor,as increased, is greater than 1, then the weighting factor is equal to1; otherwise the weighting factor is decreased; otherwise when a presentproductivity of a second product is greater than its previous maximumproductivity, then the weighting factor is decreased; otherwise theweighting factor is increased; but when the weighting factor is greaterthan 1, then the weighting factor is equal to 1; and repeating themethod at least once, wherein the weighting factor is a highest retainedvalue thereof.
 18. A method of controlling an ore treatment processincluding inoculating the ore with at least one microorganism culture,the at least one microorganism culture being used to make mineral valueswithin the ore more susceptible to extractive metallurgy recoverytechniques, the method including adjusting at least one input controlvariable and monitoring at least one output monitoring variable,comprising: establishing in an expert controller a split datadistribution for a selected input parameter having a nominal area ofunity, a mean, a standard deviation, an upper limit, and a lower limit;in response to a run of the ore treatment process, first measuring atleast one output variable in a diagnostic system; changing in an expertcontroller a value of the selected input parameter; in response to afurther run of the ore treatment process according to the changed inputparameter, second measuring the at least one output variable; and if theat least one output variable improves, in the expert controller:adjusting the split data distribution by changing the upper and lowerlimits, one of the limits being changed more than the other of thelimits; but if the at least one output variable does not improve, in theexpert controller: adjusting the split data distribution by changingonly one of the limits.
 19. The method of controlling an ore treatmentprocess according to claim 18, wherein when the at least one outputvariable comprises a plurality, the plurality including productproductivity, −P_(product), and biomass density, −P_(biomass), furthercomprising: ascribing a relationship between the product productivityand the biomass density according toP=f(P_(product))+(1−f)(P_(biomass)), wherein P is overall processproductivity and f is a weighting factor in a range from 0 to
 1. 20. Themethod of controlling an ore treatment process according to claim 19,wherein the weighting factor, f, is varied comprising: when a presentproductivity of a first product is greater than its previous maximumproductivity, then the weighting factor is increased; but when theweighting factor, as increased, is greater than 1, then the weightingfactor is equal to 1; otherwise the weighting factor is decreased;otherwise when a present productivity of a second product is greaterthan its previous maximum productivity, then the weighting factor isdecreased; otherwise the weighting factor is increased; but when theweighting factor is greater than 1, then the weighting factor is equalto 1; and repeating the method at least once, wherein the weightingfactor is a highest retained value thereof.
 21. A method of controllinga bioreactor with at least one input parameter and at least one outputparameter, comprising the steps: establishing in an expert controller adata distribution for the at least one input parameter, each of the datadistribution having an upper fixed limit and a lower fixed limit, amean, and a standard deviation; randomly changing in the expertcontroller each of the at least one input parameter, updating thestandard deviation, and calculating a change in its standard deviation;monitoring in a diagnostic system any change in the at least one outputparameter; if the change in the at least one output parameter moreclosely approximates a desired output parameter: quantifying in thediagnostic system a difference in the at least one input parameter; ifthe difference in the at least one input parameter is an increase, inthe expert controller: updating a positive standard deviation by addingthe change in the standard deviation, and updating a negative standarddeviation by subtracting the change in the standard deviation; if thedifference in the at least one input parameter is a decrease: updating apositive standard deviation by subtracting the change in the standarddeviation, and updating a negative standard deviation by adding thechange in the standard deviation; if the change in the at least oneoutput parameter does not more closely approximate the desired outputparameter: quantifying in the diagnostic system a difference in the atleast one input parameter; if the difference in the at least one inputparameter is an increase in the expert controller: updating a positivestandard deviation by subtracting the change in the standard deviation,and updating a negative standard deviation by adding the change in thestandard deviation; if the difference in the at least one inputparameter is a decrease: updating a positive standard deviation byadding the change in the standard deviation, and updating a negativestandard deviation by subtracting the change in the standard deviation;if the positive standard deviation is less than about 0.001, ascribingin the expert controller a value thereof to about 0.001; if the negativestandard deviation is less than about 0.001, ascribing in the expertcontroller a value thereof to about 0.001; and repeating the steps atleast once.
 22. The method of controlling a system according to claim21, wherein the system comprises at least one microbial strain and atleast one material to be processed, wherein either or each of the atleast one microbial strain and the at least one material to be processedis an uncharacterized microbial strain, and wherein the at least oneinput parameter includes at least one chemical, physical, or biologicalparameter.
 23. A process controller system including sub-componentscomprising: a stochastic learning algorithm that uses a split datadistribution; a sensor package; at least one set point sub-controller;an actuator package; a productivity measure comprising a set of processgoals and/or process outputs; an interconnecting communication systembetween sub-components; wherein the controller system acquiresinformation from the sensor package, calculates a productivity measure,applies the productivity measure to the stochastic learning algorithmthat uses the split data distribution, chooses at least one new setpoint to issue to the set point sub-controller, drives the actuatorpackage, and optimizes the process.
 24. The process controller systemaccording to claim 23, wherein the stochastic learning algorithmcomprises an expert system.